The Qestir do seem to have their own written language as shown in one of the Reunion sidequest lines. Traders are given a "piece of vellum with Qestiri markings" to show that they're allowed to trade in Reunion. Whether this shows that the Qestir allow for written words, or if it's simply an exception to accommodate foreign traders is up for interpretation.
Oddly enough, I read into that as being more as having, like... a wax seal of approval. There isn't actually Qestir language in long-form there, just them putting their stamp of approval on someone being there. More like a signature more than anything else, if that makes sense.
Yeah, I agree with this. The "Qestiri markings" probably refers to their tribe symbol, like the stuff we see on the banners in the steppe, or the new furniture pieces, rather than a written language exclusive to Qestir.